Lots of great tips here.
ICM ideas, effective stack sizes, keeping a good frame of mind etc.
However, I would like to add one more detail...
Define "choking" at the Final Table; what you think may be, might turn out to be the normal. Let us assume you are in a freeroll MTT with 100 players including yourself (I realize 100 may be on the very low end for an MTT, but 100 is a round number for an example with percentages later).
If everyone has the same "skill-level" (no advantage over any others), then you (one player out of 100) have a 1% chance of winning. From a statistical average, you may place in every position of the event once and only win the entire event once. This makes 9 Final Table finishes of 100 attempts. Okay, the example is incredibly unrealistic (all players are not equal in skill level, it is harder to place higher than lower in practice, variance etc.), but I think it illustrates an obvious point that is commonly overlooked:
You are not supposed to win most Final Tables you make!
It isn't necessarily choking. There is simply 9 players at the last table and someone must place 1st. 1 of 9 chance (assuming they all have equal ability - which again is a huge assumption) isn't much for you. How do you increase your chances then? Simple. Give yourself an edge over the others at the Final Table. This might be general poker ability, a better understanding of ICM pressure, more sit n' go experience etc.
The takeaway from my post (I hope) should be that not placing in 1st is not necessarily choking.